Multi-level Optimization Method Research Articles

Komagataella phaffii (Pichia pastoris) as a Powerful Yeast Expression System for Biologics Production

Komagataella phaffii (K. phaffii) (Pichia pastoris), also called biotech yeast, is a yeast species with many applications in the biotechnology and pharmaceutical industries. This methylotrophic yeast has garnered significant interest as a platform for the production of recombinant proteins. Numerous benefits include effective secretory expression that facilitates the easy purification of heterologous proteins, high cell density with rapid growth, post-translational changes, and stable gene expression with integration into the genome. In the last thirty years, K. phaffii has also been refined as an adaptable cell factory that can produce hundreds of biomolecules in a laboratory setting and on an industrial scale. Indeed, over 5000 recombinant proteins have been generated so far using the K. phaffii expression method, which makes up 30% of the total cell protein or 80% of the total released protein. K. phaffii has been used to manufacture more than 70 commercial products in addition to over 300 industrial processes that have been granted licenses. Among these are useful enzymes for industrial biotechnology, including xylanase, mannanase, lipase, and phytase. The others are biopharmaceuticals, which include human serum albumin, insulin, hepatitis B surface antigen, and epidermal growth factor. Compared to other expression systems, this yeast is also considered a special host for synthesizing subunit vaccines, which have recently been supplanted by alternative vaccination types, such as inactivated/killed and live attenuated vaccines. Moreover, efficient production of recombinant proteins is achieved through multi-level optimization methods, such as codon bias, gene dosage, promoters, signal peptides, and environmental factors. Therefore, although K. phaffii expression systems are efficient and simple with clearly established process procedures, it is still necessary to determine the ideal conditions since these vary depending on the target protein to ensure the highest recombinant protein generation. This review addresses the K. phaffii expression system, its importance in industrial and biopharmaceutical protein production, and some bioprocessing and genetic modification strategies for efficient protein production. K. phaffii will eventually continue contributing as a potent expression system in research areas and industrial applications.

Hydrodynamic responses and layout optimization of wave energy converter arrays consisting of five-degree-of-freedom truncated cylinders in front of a vertical wall

The hydrodynamic responses and layout optimization of a group of cylindrical wave energy conversion devices (WEC) in front of a fully reflecting vertical wall are investigated. Each truncated floating cylinder can oscillate with five degrees of freedom, i.e., surge, sway, heave, roll, and pitch. Based on the linear water wave theory, an analytical solution is developed for the hydrodynamic problem. The results of specific parameter studies suggest that the wall reflection effect significantly improves the energy extraction performance of the WEC array with the appropriate parameter conditions. A multi-level optimization method based on a genetic algorithm is developed. This paper investigates the optimal layout of the six WEC arrays, composed of 2–7 buoys, respectively. Additionally, the impact of other degrees of freedom (DOFs), besides the heave mode, on the hydrodynamic performance of the array is investigated. For β ≤ π/12, there is no need to consider the impact of other DOFs on the energy extraction in heave mode. The dimensionless amplitudes of other DOFs gradually decrease as the equivalent constraint stiffness increases. For k0a > 1.0, the heave amplitude and energy capture performance of the WEC array are significantly smaller. However, the amplitudes of other DOFs still have considerable magnitudes for k0a > 1.0. Therefore, for the sea area with high-frequency incident waves (k0a > 1.0), setting up a power takeoff system on other DOFs of each buoy to extract energy is a feasible solution to improve the performance of the WEC array.

Research on the lightweight design and multilevel optimization method of B‐pillar of hybrid material based on side‐impact safety and multicriteria decision‐making

AbstractThis paper designs and optimizes a new structure hybrid material B‐pillar assembly. Establish a finite element analysis model for the side impact test of an electric vehicle to verify the model's accuracy. Construct a finite element model of the hybrid material B‐pillar assembly. Combined with the static performance analysis of the B‐pillar, the laminate design of the carbon fiber composite B‐pillar reinforcement plate and optimization. For the outer and inner panels of the B‐pillar, the surrogate model method and the multiobjective optimization method are combined to set 11 design variables and 13 responses. The optimal Latin hypercube design method was used to randomly sample each design variable and fit the radial basis function (RBF) approximate model. The modified second‐generation non‐dominated sorting genetic algorithm (MNSGA‐II) was used to carry out multiobjective optimization of the mixed material B‐pillar assembly, and the multicriteria decision‐making method was used to obtain the optimal solution for the Pareto solution set. A drop weight impact test was performed on the hybrid material B‐pillar assembly. The results showed that the peak collision force of the hybrid material B‐pillar was reduced by 43.7% compared with the original steel B‐pillar, the specific energy absorption was increased by 17.5%, and the side impact safety performance was better. After optimization, the weight of the mixed material B‐column was reduced by 26.44%. The improvement rates of the intrusion amount at P2 and the intrusion speed at P1 were 23.99% and 0.63%, respectively, and the lightweight effect and side impact safety were significantly improved.Highlights The finite element analysis parameters of carbon fiber composite materials were constructed through experiments, and the basis for simulation analysis under various working conditions of the B‐pillar based on performance‐driven optimization was established. A hybrid material B‐pillar design method is proposed, which consists of a variable‐thickness high‐strength steel B‐pillar outer plate, a variable‐thickness high‐strength steel B‐pillar inner plate, and a carbon fiber composite B‐pillar reinforcement plate. The super layer of the carbon fiber composite B‐pillar reinforcement plate was optimized and the laying plan of the carbon fiber composite B‐pillar reinforcement plate was determined. Performance‐driven optimization is adopted to realize the collaboration of multilevel design and optimization methods such as B‐pillar conceptual design, detailed design, and multiobjective optimization. A modified NSGA‐II algorithm was proposed and combined with the multicriteria decision‐making method and the entropy‐weighted gray relation analysis method to determine the Pareto optimal solution and the optimal design scheme for the mixed material B‐pillar.

Design and Optimization of a Pole Changing Flux Switching Permanent Magnet Motor

A flux switching permanent magnet (FSPM) motor is designed and optimized in this paper to achieve high torque density and expanded speed regulation range from a design viewpoint of pole-changing (PC). Based on the field modulation theory, the PM field in the FSPM motor is modulated by the stator and rotor teeth, generating rich harmonics with different pole-pair numbers in the air-gap flux density. By adopting an appropriate slot pole combination, working harmonics with different slot pitch angles are obtained to establish a basis of the PC-FSPM motor. Then, different working harmonics can be used to achieve different energy conversions with different winding configurations, so the PC operation can be performed to realize the high torque and wide speed regulation range by switching the working modes. Based on the field modulation theory, the operation principle of conventional and PC-FSPM motors are analyzed and compared. Then, according to the design principle of the PC-FSPM motor, a 24/22-pole PC-FSPM motor with the E-core is designed and optimized by a multi-level optimization method. Finally, the electromagnetic performances are analyzed by finite element analysis and the test results of the prototype have verified the feasibility of the motor.

Optimal Sub-References for Setpoint Tracking: A Multi-level MPC Approach

We propose a novel method to improve the convergence performance of model predictive control (MPC) for setpoint tracking, by introducing sub-references within a multilevel MPC structure. In some cases, MPC is implemented with a short prediction horizon due to limited on-line computation capacity, which could lead to deteriorated dynamic performance. The introduced multi-level optimization method can generate proper sub-references for the MPC setpoint tracking problem, and efficiently improve the dynamic performance. In the higher level a specific performance criterion is taken as the objective, while explicit MPC is utilized in the lower level to represent the control input. The generated sub-references are then used in MPC for the real system with prediction horizon restrictions. Setpoint-tracking MPC for linear systems is used to illustrate the approach throughout the paper. Numerical simulations show that MPC with sub-references significantly improves the convergence performance compared with regular MPC with the same prediction horizon. Thus, it can be concluded that MPC with sub-references has a high potential to tackle more complicated control problems with limited computation capacity.

Lightweight design method and application of MEWP bracket based on multi-level optimization

<abstract> <p>Mobile elevating work platform (MEWP) is a large-scale engineering machinery equipment that transports workers and tools to the designated height for operation. As the key supporting component of MEWP, the bracket simultaneously needs to meet the performances of high stiffness and strength. Furthermore, the mechanical performance of the bracket can be significantly influenced by its cross-sectional shape. However, the optimal cross-sectional shape of bracket is not easily to obtain owing to the lacking of lightweight design method. Thus, a lightweight design method of MEWP bracket based on multi-level optimization is proposed in this paper. Firstly, the multi-case topology optimization model of MEWP bracket is constructed by using the compromise programming method, and the optimal section configuration of MEWP bracket is obtained based on Solid Isotropic Material with Penalization (SIMP). Secondly, the parameterization of the cross-sectional shape of bracket is realized using the mesh deformation technology, and the multi-case optimization mathematical model of the MEWP bracket is established. Then, the cross-sectional shape and gauge of the bracket are optimized using multi-level optimization method. The optimized results show that weight reduction mass is 11.66 kg and the ratio is 52.4% under the premise that the stiffness of the bracket does not decrease. Furthermore, the weight of MEWP bracket optimized by the multi-level optimization method reduced by 1.27 kg compared with single gauge optimization method. Finally, a physical prototype is developed according to the optimization results.</p> </abstract>

Analysis and design optimization of a low-cost axial flux Vernier machine with SMC cores and ferrite magnets

In this paper, a low-cost high-performance axial flux Vernier machine (AFVM) with soft magnetic composite (SMC) cores and ferrite magnet is proposed, analyzed and optimized. By cooperating with spoke magnet rotor configuration and 3D magnetic flux stator structure, the proposed AFVM can output higher torque compared with the traditional permanent magnet machine though low-cost low-energy-density ferrite magnet and low-permeability SMC material are adopted. The main electromagnetic topology and operation principle of the proposed AFVM are introduced; then, its main dimensions are investigated and optimized by using sequential optimization method. Moreover, a new multilevel Taguchi design optimization which is an improvement of multilevel optimization is proposed for the torque and power factor optimization. Lastly, its main performance of AFVM optimized by the sequential optimization method and multilevel Taguchi design optimization method has been compared with a normal axial flux machine in terms of torque ability, power factor and efficiency based on 3D finite element method.

Локалізація ексергетичних втрат в утилізаторі теплоти відхідних газів газоспоживальних теплових установок

The problem of increasing the thermodynamic efficiency of power plants can be solved only by using a complex approach using methods based on modern methods of exergy analysis in combination with methods of heat transfer theory, theory of linear systems, structural-variant methods, multi-level optimization methods, etc. The analysis of the possibility of applying the discrete-modular principle and the corresponding complex method for analyzing the efficiency of the exhaust gases heat-recovery exchanger of a cogeneration unit heat engine is performed in the paper. The aim of the work is to analyze the localization of exergy losses, their differentiation, and the establishment of the relative contribution of various types of losses to the general exergy losses in the exhaust gases heat-recovery exchanger of a cogeneration unit heat engine. The structural features of the heat-recovery exchanger and the exergy properties that reflect the essence of exergy methods: universality and additivity, made it possible to use the discrete-modular principle and a complex method based on exergy-dissipative functions for efficiency analysis. The advantage of this method is the ability to analyze the localization of exergy losses in separate modules of the heat-recovery exchanger and to differentiate the exergy losses associated with nonequilibrium heat transfer between the heat-transfer agents and the wall, heat conduction and the movement of heat-transfer agents. Using the chosen complex method, the analysis of the localization of exergy losses in the heat-recovery exchanger was carried out and the exergy-dissipative functions of each of the eight modules of the heat-recovery exchanger were calculated. Differentiation of exergy losses was carried out and the relative contribution of exergy losses associated with the processes of heat transfer from flue gases to the wall, from wall to water, in heat conduction processes, as well as exergy losses associated with the movement of heat-transfer agents, in the general exergy losses was analyzed. To determine the exergy losses due to nonequilibrium heat transfer between the heat-transfer agents and the motion of the heat-transfer agents, the differential exergy equations, the equations for the heat flow densities between the heat-transfer agents and the wall, the equation for the heat flow density due to heat conduction through the wall and the equations of motion are used. It has been established that the localization of maximum exergy losses in all modules of the heat-recovery exchanger is associated with losses due to heat transfer from flue gases to the wall.

On a multilevel Levenberg–Marquardt method for the training of artificial neural networks and its application to the solution of partial differential equations

In this paper, we propose a new multilevel Levenberg–Marquardt optimizer for the training of artificial neural networks with quadratic loss function. This setting allows us to get further insight into the potential of multilevel optimization methods. Indeed, when the least squares problem arises from the training of artificial neural networks, the variables subject to optimization are not related by any geometrical constraints and the standard interpolation and restriction operators cannot be employed any longer. A heuristic, inspired by algebraic multigrid methods, is then proposed to construct the multilevel transfer operators. We test the new optimizer on an important application: the approximate solution of partial differential equations by means of artificial neural networks. The learning problem is formulated as a least squares problem, choosing the nonlinear residual of the equation as a loss function, whereas the multilevel method is employed as a training method. Numerical experiments show encouraging results related to the efficiency of the new multilevel optimization method compared to the corresponding one-level procedure in this context.

A novel techno-economic multi-level optimization in home-microgrids with coalition formation capability

In recent years, microgrids (MGs) have operated in the power systems for various reasons such as reduction of energy losses, improvement of voltage stability and grid reliability. The implementation of Home Microgrid (H-MG) has proven successful in tackling these issues. This paper proposes a novel techno-economic multi-level optimization method and modern time varying price model aimed at encouraging participation in a coalition system, minimizing energy cost of a Home Microgrid (H-MG) and investigate the impact it has on voltage stability and reliability of the grid. The intended H-MG includes an apartment with several units which consist of electrical and thermal energy generators, energy storage devices and can trade energy within the H-MG's and the upstream network. The proposed method develops an algorithm for smart charging/discharging of energy storage and electric vehicles (EV) to improve energy efficiency. The performance of the proposed algorithm is tested on several electrical and thermal loads configurations, the IEEE 15 and 33-bus networks are used to prove the efficiency of the coalition system between the H-MG on a large scale. The simulations are implemented on MATLAB software and results indicate an improvement in voltage profiles and grid reliability.

A Critical Survey of the Multilevel Method in Complex Networks

Multilevel optimization aims at reducing the cost of executing a target network-based algorithm by exploiting coarsened, i.e., reduced or simplified, versions of the network. There is a growing interest in multilevel algorithms in networked systems, mostly motivated by the urge for solutions capable of handling large-scale networks. Notwithstanding the success of multilevel optimization in a multitude of application problems, we were unable to find a representative survey of the state-of-the-art, or consistent descriptions of the method as a general theoretical framework independent of a specific application domain. In this article, we strive to fill this gap, presenting an extensive survey of the literature that contemplates a systematic overview of the state-of-the-art, a panorama of the historical evolution and current challenges, and a formal theoretical framework of the multilevel optimization method in complex networks. We believe our survey provides a useful resource to individuals interested in learning about multilevel strategies, as well as to those engaged in advancing theoretical and practical aspects of the method or in developing solutions in novel application domains.

A Study on Stacking Sequence Design of Composite Fan Blades Using Multi-level Optimization

In this paper, the multi-level optimization method is proposed to design the optimal stacking sequence of composite fan blade more efficiently. The fan blade model used is a laminate with inconsistent stiffness because the thickness is not uniform throughout the model. This feature complicates the optimization problem and makes it difficult to apply optimal design algorithms that use only continuous or discrete variables. For this reason, we conducted the literature survey about combining the optimal design algorithm with continuous and discontinuous variables and developed optimization algorithm for the composite fan blade. Moreover, the design space of discrete variables is reduced through the optimal design of continuous variables. In the first-level, response surface method is used, with the design variables being the volume fraction of plies of the predefined angles of [0°/±45°/90°]. The optimization problem in the first-level aims at minimizing the tip displacement of the fan blade and constraints on other structural responses are imposed. At the second-level, the permutation genetic algorithm is used with the fiber orientation of each ply as design variables. In this level, we perform the optimal design of the stacking sequence using the results determined by prior level, while the composite design rule and compliance constraints are applied.

Newton-type multilevel optimization method

Inspired by multigrid methods for linear systems of equations, multilevel optimization methods have been proposed to solve structured optimization problems. Multilevel methods make more assumptions regarding the structure of the optimization model, and as a result, they outperform single-level methods, especially for large-scale models. The impressive performance of multilevel optimization methods is an empirical observation, and no theoretical explanation has so far been proposed. In order to address this issue, we study the convergence properties of a multilevel method that is motivated by second-order methods. We take the first step toward establishing how the structure of an optimization problem is related to the convergence rate of multilevel algorithms.

A Multi-Level Optimization Method for Elastic Constants Identification of Composite Laminates

A new and effective elastic constants identification technique is presented to extract the elastic constants of a composite laminate subjected to uniaxial tensile testing. The proposed technique consists of a new multi-level optimization method that can solve different types of minimization problems, including the extraction of material constants of composite laminates from given strains. In the identification process, the optimization problem is solved by using a stochastic multi-start dynamic search minimization algorithm at the first level in order to obtain the statistics of the quasi-optimal design variables for a set of randomly generated starting points. The statistics of the quasi-optimal elastic constants obtained at this level are used to determine the reduced feasible region in order to formulate the second-level optimization problem. The second-level optimization problem is then solved using the particle swarm algorithm in order to obtain the statistics of the new quasi-optimal elastic constants. The iteration process between the first and second levels of optimization continues until the standard deviations of the quasi-optimal design variables at any level of optimization are less than the prescribed values. The proposed multi-level optimization method, as well as several existing global optimization algorithms, is used to solve a number of well-known mathematical minimization problems to verify the accuracy of the method. For the adopted numerical examples, it has been shown that the proposed method is more efficient and effective than the adopted global minimization algorithms to produce the exact solutions. The proposed method is then applied to identify four elastic constants of a [0°/±45°]s composite laminate using three strains in 0°, 45°, and 90° directions, respectively, of the composite laminate subjected to uniaxial testing. For comparison purposes, several existing global minimization techniques are also used to solve the elastic constants identification problem. Again, it has been shown that the proposed method is capable of producing more accurate results than the adopted available methods. Finally, experimental data are used to demonstrate the applications of the proposed method.

Floor Frame Structure Conceptual Design of Car Body by Multi-level Optimization Method

To optimize the floor structure of car body in conceptual design phase, a discrete topo optimization method is implemented. First of all, by several body beam section parameters are collected and simplified as rectangular beam cross section. The parameterized simulation model of concept car body structure is modeled with simplified beams. The floor general structure is determined and redefined the discrete topology domain of car body floor, solves the coupling relations between two kinds of design variables which are topology of the floor beam and connection position of floor beam, through the construct platform and conversion of optimization goals and design constraints between different levels, the multi-island genetic algorithm (MIGA) algorithm was used to seek the optimal solution and fully verifies its accuracy by examples.

COMPREHENSIVE METHODS OF EVALUATION OF EFFICIENCY AND OPTIMIZATION OF HEAT-UTILIZATION SYSTEMS

At present, Ukraine has the necessary potential for the implementation of effective energy-saving technologies for heat recovery, and therefore the problem of their development and implementation is relevant for the country's energy sector. The solution of this problem is related to the need for systematic studies of the efficiency of optimization of heat recovery facilities from the standpoint of modern methodological approaches. The paper outlines the main stages in the development of integrated methods for assessing the efficiency and optimization of heat recovery systems based on the principles of exergic analysis, statistical methods for planning the experiment, structured variational methods, multilevel optimization methods, the theory of linear systems and the thermodynamics of irreversible processes. Examples and illustrations illustrate some of the stages in the development of complex methods. The necessary general step in the development of methodologies is the development of new performance criteria. Such criteria are highly sensitive to changes in the regime and design parameters of heat recovery systems due to the inclusion of some exergic characteristics in them. The developed criteria also serve as target optimization functions. For individual elements of heat recovery systems, efficiency and optimization methods usually include the definition of the functional dependencies of the selected efficiency criteria on the main parameters. For this, balance methods of exergic analysis and statistical methods of experiment planning are used. If such dependencies are established, optimization is carried out using known mathematical methods. For complex heat recovery systems involving a large number of elements, it is not possible to establish general analytical dependencies of the optimization objective functions on the parameters of the system when constructing mathematical models necessary for their optimization. Complex methods based on the basic principles of structural-variant methods, methods of multilevel optimization, the theory of linear systems, and the thermodynamics of irreversible processes have been developed for such cases. For this purpose, structural diagrams of plants, block diagrams of multi-level optimization have been developed, complete input matrices have been constructed, mathematical models for the processes under investigation have been developed, formulas have been derived for calculating the loss of exergy power in heat conduction processes and formulas for calculating dissipators of exergy. A well-founded choice of the methodology for evaluating efficiency and optimization raises the effectiveness of optimization, since it allows the use of parameters maximally close to optimal when developing the heat recovery system design, which in turn increases the efficiency of the system. References 14, figures 5.

Estimation of Manning roughness coefficient for vegetated furrows

Manning’s roughness coefficient is one of the most important parameters in the design and evaluation of surface irrigation. In this study, Manning’s roughness coefficient was evaluated under two different inflow discharges (i.e., 0.29 and 0.44 L s− 1) on vegetated furrow irrigation during maize growing season. In addition, the accuracy of multilevel optimization and SIPAR-ID methods was evaluated for the estimation of Manning’s roughness coefficient and infiltration equation parameters in vegetated furrows. Spacing, length, and longitudinal slope of experimental furrows were 0.75 m, 110 m, and 1.2%, respectively. Values of the Manning’s roughness coefficient in the vegetated furrows increased as compared to its recommended values in bare furrows. On the contrary, inflow discharge had a weak inverse impact on Manning’s roughness coefficient. Roughness coefficient was the highest at downstream section (end) of the experimental furrow and its value at the middle section was higher than that of upstream section. The results also indicated that the multilevel optimization method had a good performance with average relative error (RE) about 5% for both discharges and SIPAR-ID method had an approximately proper estimation with relative error ranging from 4.6 to 15% in estimating Manning’s roughness coefficient for all irrigation events. To estimate the infiltrated volume of water into soil, the multilevel optimization method had a very good performance (RE = − 1.65 to 2.81%).

WEIGHT MINIMIZATION OF SHIP CHAMBER STRUCTURE IN VERTICAL SHIP LIFT DESIGN BASED ON MULTI-LEVEL STRUCTURAL OPTIMIZATION METHOD

Weight reduction of ship chamber is a main concern of ship lift design for improving the load capacity. The structure of ship chamber is typical of beam-plate structure. To deal with structural optimization problem of beam-plate structure, a multilevel structural optimization method was developed based on combining an improved bi-directional evolutionary structural optimization (BESO) method and surrogate model method, which covers three optimization levels, as dimension optimization, topology optimization and section optimization. The aim of the proposed optimization method is to determine global design parameters, integral structural topology, and locations and sectional parameters of structural members from an oversized ground structure. The kernel optimization procedure (KOP) is using BESO to obtain the optimal topology from a ground structure. In order to deal with beam-plate structures, cubic box is adopted as the unit cell to construct ground structure for BESO. In the first optimization level, based on different dimensional parameter combinations, a series of ground structures are generated and used to perform KOP. Response surface (RS) model is used to simulate the nonlinear relationship between the optimal objective values and dimension parameters, then the optimal dimensional parameters can be obtained. In the second optimization level, the optimal dimension parameters are used to generate the ground structure, and the optimal topology could be obtained by using KOP. In the third optimization level, RS model is also used to determine the section parameters. The proposed method is applied to structural design of ship chamber of a 500-ton class ship lift. The results show that the proposed method leads to a greater weight saving, compared with the original design and generic algorithm (GA)-based optimization results.

Ефективність комбінованих теплоутилізаційних систем котельних установок (частина 2)

Для комбінованої теплоутилізаційної системи котельної установки, призначеної для підігріву води та підігріву і зволоження дуттєвого повітря, наведено результати аналізу ефективності і оптимізації, проведеного на основі розроблених методик, першу з яких засновано на поєднанні елементів ексергетичного аналізу із структурно-варіантними методами, а другу - на поєднанні елементів ексергетичного аналізу з методами багаторівневої оптимізації. Для поверхневого конденсаційного водопідігрівача та контактного підігрівача і зволожувача повітря, що входять до складу теплоутилізаційної системи, наведено результати проведеної в рамках розробленої методики, яка включає структурно-варіантні методи, оптимізації режимних і конструкційних параметрів. На основі розробленої методики, яка включає методи багаторівневої оптимізації, отримано оптимальні значення режимних та конструкційних параметрів для зазначеної теплоутилізаційної системи. При застосуванні вказаних методик розраховано відповідні значення критеріїв ефективності теплоутилізаційної системи. Порівняльний аналіз вказаних методик показав, що критерій ефективності теплоутилізаційної системи, отриманий при застосуванні методики, яка включає методи багаторівневої оптимізації, приблизно на 2% нижче, ніж критерій ефективності, отриманий при використанні методики, яка включає структурно-варіантні методи. Одержані результати свідчать про те, що при застосуванні методики, яка включає методи багаторівневої оптимізації, режимні та конструкційні параметри теплоутилізаційної системи максимально наближені до оптимальних і відповідно ефективність теплоутилізаційної системи вище. Ключові слова: теплоутилізаційна система, методи оптимізації, критерії ефективності

A multilevel optimal method and its engineering application for heterotypic space grid structure

The heterotypic space grid structure (HSGS) is featured with complex mechanical behavior, a variable structural shape and a strong correlation relationship among structural parameters. HSGS's optimization has always been a challenging subject. By studying geometrical characteristics and mechanical behavior of HSGS, a multilevel optimization method was proposed to minimize the HSGS weight. In the first stage, the strength and stability of HSGS members were optimized in the local constraint. In the second stage, the overall stiffness and stability of HSGS were optimized in the overall constraint. The computational optimization method for HSGS was realized by combining the discrete variable optimization design theory with the relative difference quotient algorithm. The multilevel optimization method of HSGS was programmed by using the ANSYS parameterized language. The validity of the optimization method and program were testified by comparing the results of a real engineering case from the multilevel optimization method with the results of the MST software.